Exhaust gas after-treatment system

ABSTRACT

An exhaust gas after-treatment system ( 10 ) for a gasoline engine ( 12 ) has a three-way catalyst ( 14 ) close-coupled to the gasoline engine, a particulate matter control device ( 18 ) positioned downstream of the three-way catalyst, a NOx control system ( 16 ) positioned downstream of the particulate matter control device. According to one method of operation, the gasoline engine is operated in a stoichiometric condition upon start-up of the engine, the exhaust gas flow generated by the engine is conducted through the exhaust system, and then the gasoline engine ( 12 ) is operated in a lean-burn condition after the NOx control system ( 16 ) attains a minimum operating temperature.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of priority to U.S. provisional application No. 61/154,544, filed on Feb. 23, 2009.

FIELD

The disclosure relates generally to engine exhaust after-treatment systems, and more particularly to porous honeycomb ceramics used in catalytic converters and particulate filters of engine exhaust after-treatment systems.

BACKGROUND

There is an emphasis on improved vehicle fuel economy and emissions. For gasoline engines with spark ignition, injection of gasoline directly into the cylinder provides fuel economy benefits due to several factors including charge cooling which allows for higher compression ratio, and more precise control of fuel especially for start and stop driving modes. In addition when operated under lean burn combustion conditions, direct injected spark ignition (DISI) gasoline engines (also sometimes variously referred to as “lean direct injection spark ignition,” “lean DISI,” “lean gasoline direct injection,” or “lean GDI”) offer further fuel economy benefits at reasonable cost. In particular, gasoline DISI engines for passenger car automotive and medium-duty vehicle applications offer greater power output and higher fuel economy compared to conventional multi-port fuel injection engines. However, lean DISI engines have two emission issues that must be addressed: the difficulty of converting NOx under excess oxygen conditions by conventional three-way catalyst systems, and production of relatively high levels of ultra-fine (e.g., nanometer sized) particulate matter (PM). Stoichiometric gasoline engines also produce significant amounts of nanometer sized particulate matter.

With respect to generation of particulate matter, DISI engines produce carbon soot as a component of their exhaust emissions. The emission of ultra-fine particles into the atmosphere is considered a health issue due to the respiration of these particles into the lungs of people. In addition, the production of carbon black particles is thought to contribute to global climate change. Although the total mass of soot produced and the number of ultra-fine particles emitted by DISI engines is generally lower than those produced by diesel engines (measured, for example, as mass or number of particles emitted per distance driven or per time operated), it is significantly higher than emissions from port-fuel injected gasoline engines, and from diesel engines equipped with particle filtration devices. Thus an exhaust after-treatment filtration system that reduces the emission of ultra-fine particles from vehicles that are powered by DISI engines is desirable.

SUMMARY

One aspect of embodiments described herein provide an exhaust gas after-treatment system for a gasoline engine comprising a three-way catalyst close-coupled to the gasoline engine; a particulate matter control device positioned downstream of the three-way catalyst; and a NOx control system positioned downstream of the particulate matter control device.

In another aspect, embodiments described herein provide a method for cleaning an engine exhaust gas flow, comprising: operating a gasoline engine in a stoichiometric condition upon start-up of the engine; conducting an exhaust gas flow generated by the engine through an exhaust system comprising, successively, a flow-through substrate having a three-way catalytic coating, a wall-flow particulate filter, and a NOx control system; and operating the gasoline engine in a lean-burn condition after the NOx control system attains a minimum operating temperature.

Additional features and advantages will be set forth in the detailed description which follows, and in part will be readily apparent to those skilled in the art from that description or recognized by practicing the embodiments as described herein, including the detailed description which follows, the claims, as well as the appended drawings.

It is to be understood that both the foregoing general description and the following detailed description present embodiments that are intended to provide an overview or framework for understanding the nature and character of the invention as it is claimed. The accompanying drawings are included to provide a further understanding of the invention as it is claimed, and are incorporated into and constitute a part of this specification. The drawings illustrate various embodiments and, together with the description, serve to demonstrate the principles and operations of the invention as it is claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration of one embodiment of an exhaust gas after-treatment system for a gasoline engine.

FIG. 2 is a schematic illustration of another embodiment of an exhaust gas after-treatment system for a gasoline engine.

DETAILED DESCRIPTION

Reference will now be made in detail to embodiments demonstrating principles and operations of the invention as it is claimed, examples of which are illustrated in the accompanying drawings. Whenever possible, the same reference numerals will be used throughout the drawings to refer to the same or like parts.

As used herein, the term “stoichiometric” combustion means the point at which the air to fuel ratio is such that the fuel is fully oxidized with no remaining oxygen. For example, stoichiometric combustion in gasoline engines typically occurs at an air-fuel mass ratio of about 14.7:1, although it will be recognized by those skilled in the art that the air-fuel ratio in stoichiometric gasoline cars equipped with three-way catalysts require a small oscillation of air-fuel ratio about the stoichiometric point. As used herein, “lean” combustion conditions result when the air to fuel ratio during combustion is greater than at the stoichiometric point (i.e., excess air), while “rich” combustion conditions result when the air to fuel ratio during combustion is less than at the stoichiometric point (i.e., excess fuel). Exhaust gases resulting from lean combustion include excess oxygen and relatively small amounts of NOx, hydrocarbons, and carbon monoxide due to nearly complete combustion of the hydrocarbon fuel.

Proposed regulations set forth both particle number and particle mass based limits for gasoline engines. For example, Euro 6 regulations slated for implementation in 2014 limit particle number and mass based emissions to 6×10¹¹ particles/km and 4.5 mg/km, respectively, based on the NEDC regulatory drive cycle and the PMP test protocols for particulates measurement. Independent testing by the inventors of currently available vehicles having lean burn DISI technology (i.e., a 2007 Mercedes CLS350 CGI having a V6 engine with twin exhaust, and a 2007 BMW 120i having a 4 cylinder single exhaust line) show typical particle-based emissions in the range of about 2×10¹² to about 4×10¹² particles/km and mass-based emissions of about 2 to about 2.5 mg/km, which meet current regulatory requirements but do not meet the more stringent particle number based limits in the proposed Euro 6 regulation. Notably, the independent testing by the inventors indicates that current exhaust after-treatment systems of the test vehicles have no effect on particle number or mass based emissions. That is, current after-treatment systems for spark ignition DISI engines do not appreciably reduce particle number or particle mass emissions. Accordingly, new product designs and system configurations for after-treatment of exhaust gases from spark ignition DISI engines are required for acceptable after-treatment results.

Exhaust after-treatment systems for removing particulate matter from diesel engine exhaust are well known. However, and notably, there are several technical differences in the make-up of the exhaust gas, the exhaust conditions, and engine operating conditions of DISI and diesel engines such that it is not possible to directly apply diesel after-treatment technology to gasoline engines. For example, DISI engines operate in both stoichiometric and lean-burn modes, while diesel engines operate only in lean-burn. Compression ratios of DISI engines are generally less than 12 (although the compression ratio of some high performance engines may be as high as 15), while the compression ratios of diesel engines are much higher, making DISI engines more sensitive to exhaust system backpressure. As further differences, the temperature of DISI engine exhaust is generally higher than the temperature of diesel engine exhaust, the volume of exhaust gas from a DISI engine is generally higher than a comparably sized diesel engine, and the generation of particulate matter and NOx differs for DISI and diesel engines.

With respect to particulate matter generation, solid soot particles produced by DISI engines are smaller than solid soot particles produced by diesel engines. It is theorized that the particle size difference may be caused by factors such as differences in fuel chemistry, molecular weight, and combustion dynamics. Differences in the aerosolized particulate matter (e.g. liquid droplets) produced by DISI engines also exist, but are less known. In addition, soot production rates of lean DISI engines are significantly (i.e., about an order of magnitude) lower than soot production rates of diesel engines. As a result, the soot accumulation rate in a particulate filter used in a DISI system is expected to be much lower than the soot accumulation rate in a diesel system. This means that the need for frequent filter regeneration is reduced in DISI systems, or that filter regeneration can be initiated at much lower soot loading levels than required in a diesel system.

With respect to NOx generation, NOx levels produced by DISI engines are higher than those of diesel engines due to the DISI engine's higher cylinder combustion temperature. The ratio of NOx to carbonaceous soot in the exhaust is an important factor in passive filter regeneration (via the reaction of 2NO₂+C→CO₂+2NO). In a gasoline engine the NOx to soot ratio is higher than in a diesel engine. Combined with the higher average exhaust temperatures of gasoline engines, the amount of passive regeneration of carbonaceous soot by nitrogen dioxide (NO₂) is relatively high, and consequently the soot accumulation rate in a gasoline system is even lower than in a diesel system. Gasoline engines can also be operated at exhaust temperatures whereby continuous oxidation of soot by oxygen occurs when temperatures in the filter exceed about 600° C. and excess O₂ is present.

As will be described in further detail, the present disclosure provides embodiments of exhaust after-treatment systems suitable for gasoline engines in general, and gasoline direct injection (DISI) engines in particular, that operate in both stoichiometric and lean modes, some of such embodiments including particulate filters having relatively low thermal mass (as compared to existing diesel filters). In some embodiments, filter wall thickness, inherent material density, total porosity, and product length to diameter ratios are manipulated to control thermal mass and/or pressure drop.

Referring now to FIG. 1, a schematic illustration of an exhaust after-treatment system 10 for a DISI engine 12 is provided. After-treatment system 10 includes a close-coupled catalyst 14 (e.g., a three-way catalyst (TWC)), a NOx control system 16 (e.g., a lean NOx trap (LNT)) 16, and a particulate matter control device 18 (e.g., a wall-flow filter) connected to each other via an exhaust pipe 20. As will be discussed in further detail below, other embodiments of after-treatment systems may include additional components, such as additional or different NOx control systems, and/or the components may be arranged in different orders.

In one embodiment, at least one of close-coupled catalyst 14, NOx control system 16, and particulate filter 18 comprise a honeycomb body. In one embodiment, all of close-coupled catalyst 14, NOx control system 16, and particulate filter 18 comprise honeycomb bodies. In one embodiment, at least one of close-coupled catalyst 14, NOx control system 16, and particulate filter 18 comprise a ceramic body. In one embodiment, all of close-coupled catalyst 14, NOx control system 16, and particulate filter 18 comprise ceramic bodies.

Three-way catalysts (TWC) are designed to simultaneously convert three pollutants to harmless emissions: reduction of nitrogen oxides to nitrogen and oxygen, oxidation of carbon monoxide to carbon dioxide, and oxidation of unburned hydrocarbons (HC) to carbon dioxide and water. Suitable catalyst formulations include three-way compositions having an oxygen storage component such as cerium oxide, and precious metals such as palladium, platinum, or rhodium.

To determine the efficacy of various embodiments of particulate matter control devices for use in DISI after-treatment systems, filters and substrates having a range of properties and configurations were tested in an exhaust after-treatment system 10 as illustrated in FIG. 1. Filtration efficiency testing was carried out using Differential Mobility Scanner (DMS) particle size and concentration measurement equipment with a BMW 118i direct injection, spark ignited engine running on a test stand.

Referring to Table 1, nine different particulate matter control devices are referenced (Samples A-I). Samples A-G and I comprise ceramic materials, while sample H comprises a metal material having a tortuous path flow-through type configuration (PM-Metalit™ available from Emitec). Samples A-E and G are configured as wall-flow filters. At the nano-particle level that is characteristic of DISI engine particulate matter, the efficacy of flow-through substrates for reducing particulate matter was unknown. Thus, samples F and I were configured as flow-through substrates to determine whether the number and mass of particulates might be reduced by a high performance emission substrate. Sample F provided a discontinuous channel wall, while Sample I provided a continuous channel wall. In principal, soot can be oxidized by the reactions: C+O₂→CO₂ and C+½O₂→CO. Thus, sample I was coated with a catalytic material to determine the efficacy of substrates for reducing particulate matter through catalytic oxidation. Specific materials and geometries (cell density, wall thickness, porosity, median pore size, diameter and length) of the samples are provided in Table 1.

Using the configuration of FIG. 1, particulates were measured in the exhaust gas prior to and immediately after the particulate matter control device 18. Candidate particulate matter control devices were positioned after existing close-coupled and underbody catalysts and the NOx sensor used in the commercial BMW 118i exhaust system. To facilitate testing, the mufflers were removed from the exhaust system. Candidate particulate matter control devices were canned using a modular canning design and standard mat materials. Taps for pressure, temperature, and gas analyzer measurements were provided for measurements upstream and downstream of the particulate matter control device 18. Filtration efficiency and pressure drop were measured at both low and high exhaust gas flow rates of approximately 18 and 72 kg/hr respectively.

Table 1 summarizes results from the filtration efficiency testing. The measured filtration efficiencies in Table 1 are based on accumulation mode particle numbers (e.g. the number of carbonaceous soot and inorganic ash particles). As seen from the data presented in Table 1, full wall-flow filters (i.e., samples A-E and G), as compared to partial filters (i.e., samples H) or flow-through substrates (i.e., samples F and I), are effective for the reduction of particle number emissions from DISI engines operating under lean burn or lean-switching (i.e., switching between stoichiometric and lean) conditions. Calculations indicate that filtration efficiencies greater than about 92% are required to meet the proposed Euro-6 particulate matter regulations if such regulations were applied to the 2007 Mercedes CLS350 and BMW 120i & 118i vehicles.

The measured filtration efficiencies set forth in Table 1 demonstrate that wall-flow filters of a variety of materials, including aluminum titanate, cordierite, and silicon carbide, can sufficiently reduce particle number emissions to meet or exceed the proposed Euro-6 levels. If catalyzed, such wall-flow filters can additionally be effective for reduction of gaseous emissions of hydrocarbons, CO, and NOx. However, flow-through substrates and partial filters alone are not sufficiently effective for particle number or particle mass reduction.

Viewing the results of Table 1, it can be seen that wall-flow filters with cell densities in the range of 200 to 600 cells per square inch (cpsi) and thin walls (i.e., less than about 0.020 inch (mil) and as thin as about 0.003 inch) have an excellent combination of high filtration efficiency (i.e., greater than about 90% filtration efficiency) and low pressure drop when used as bare filters (i.e., not catalyzed). The results in Table 1 further demonstrate that reducing wall thickness generally leads to decreasing pressure drop, while increasing cell density leads to increased pressure drop. Suitable wall flow filters have total wall porosity in the range of about 30% to about 60%. Wall-flow filters with high cell densities and thin walls (such as the 600 cpsi, 3 mil wall thickness of sample G) provide the necessary filtration efficiency, but at the penalty of a higher pressure drop. Because of their higher geometric surface area, bodies with high cell densities (i.e., over about 300 cpsi in one embodiment) will have utility as coated or catalyzed components, thereby providing multi-functional devices having both particulate matter filtration and HC/CO/NOx emission control features in DISI engine emission after-treatment systems.

FIG. 2 shows an exhaust system configuration used to further test the performance of uncatalyzed wall flow filter devices with gasoline engines. In particular, an exhaust system 100 for direct injection gasoline engine 12 includes a close-coupled catalyst 14, particulate matter control device 18, and NOx control system 16. For testing purposes, a supplementary NOx catalyst 16′ was installed in the system 100 of FIG. 2 to maximize the ratio of NO₂ to NO via the interconversion of these species by reaction with oxygen. NOx control system 16 is selected from any suitable NOx control technology such as, for example, a lean NOx trap (LNT), a lean NOx catalyst (LNC), a selective catalytic reduction (SCR) system, or a combination of one or more of these or other NOx control systems.

Lean NOx traps (LNT) work by absorbing nitrogen oxides (NOx) from exhaust gas and releasing the stored NOx in an atmosphere containing less oxygen for reduction to di-nitrogen (N2) in a separate regeneration step. Exemplary NOx-absorbents are often associated with a catalyst for oxidizing nitrogen monoxide (NO) to nitrogen dioxide (NO₂), e.g. platinum (Pt), and, optionally, also a catalyst such as rhodium, for reducing NOx to N2 with a suitable reductant (e.g., a hydrocarbon) especially when the system operates close to stoichiometric conditions.

Lean NOx catalysts (LNC) work by using hydrocarbons as NOx reductants. The hydrocarbons may be those naturally present in the exhaust gas (i.e., “native” hydrocarbons) or hydrocarbons may be added to the exhaust gas. LNC catalysts must be selective for NOx reduction compared to competing reactions that might oxidize the hydrocarbons to CO₂ and water thus rendering them unable to facilitate conversion of NOx to di-nitrogen.

Selective catalytic reduction (SCR) catalysts work by chemically reducing NOx (NO and NO₂) to nitrogen (N₂). When used in a lean gas stream, a reductant is added to the system to enable the reaction. Ammonia or an ammonia precursor (e.g., aqueous urea) is the primary reductant used in SCR systems. Ammonia-SCR systems react ammonia (NH₃) with the NOx to form nitrogen (N₂) and water (H₂O).

Suitable de-NOx formulations include the use of barium oxide with platinum for lean-NOx reduction, or SCR systems based on zeolites such as ZSM-5, Zeolite Beta, ZSM-35, ZSM-12, mordenite, faujasite Y-type zeolite, ferrierite, chabazite, or alternatively SCR with base metal oxide systems using tungsten, vanadium, and titanium oxides.

Referring again to FIG. 2, in one embodiment, the close-coupled catalyst 14 has a cell density in the range of about 400 cpsi to about 900 cpsi, a web thickness in the range of about 2 mil to about 4 mil, platinum group metals (PGM) coating formulation, and alumina, zirconia, or ceria wash coat having oxygen storage capability.

In one embodiment, particulate matter control device 18 has a cell density in the range of about 200 cpsi to about 600 cpsi, and a web thickness in the range of about 3 mil to about 15 mil. Cell densities at the higher end of the range (e.g., in excess of about 300 cpsi) are preferred when particulate matter control device 18 is to provide both particulate matter filtration and HC/CO/NOx emission control features (i.e., when particulate matter control device 18 is to be coated or catalyzed). Total porosity of particulate matter control device 18 is greater than about 30%, and may approach about 60-65% when particulate matter control device 18 is to be coated or catalyzed. In one embodiment, particulate matter control device 18 is provided with a length to diameter (L:D) in the range of about 0.5 to about 2. In some embodiments, the particulate matter control device 18 may be provided with an asymmetric cell design (i.e., inlet channels having a larger hydraulic diameter than outlet channels) for increased ash capture and storage to extend the life of the filter. In one embodiment, the ratio of inlet hydraulic diameter to outlet hydraulic diameter is in the range from about 1.1:1 to about 1.5:1.

As noted above, in some embodiments, particulate matter control device 18 provides a catalytic functionality in addition to filtering particulates from the exhaust stream. In one embodiment, particulate matter control device 18 is provided with a platinum group metals (PGM) coating formulation. In one embodiment, particulate matter control device 18 has an alumina, zirconia, or ceria washcoat, or combinations thereof, having oxygen storage capability. In one embodiment, particulate matter control device 18 has a lean NOx trap (LNT) functionality provided by, for example, barium oxide. In one embodiment, washcoats and catalysts are preferentially located within particulate matter control device 18, such as near the inlet side of the device.

Cold-start emissions control in a gasoline engine can be particularly challenging while waiting for emission control components to reach the minimum operating temperatures required for catalytic conversion of undesired exhaust gas components. This challenge grows as the amount of catalyst and substrate mass in the exhaust system increases. A primary function of close-coupled catalyst 14 is to control emissions from engine 12 during the first minutes of engine start-up (i.e., cold-start emissions). In most instances, at start-up, engine 12 will operate under stoichiometric conditions. The near engine position of close-coupled catalyst 14 allows close-coupled catalyst 14 to quickly reach operating (i.e., light-off) temperatures and begin converting at least about 90% of the hydrocarbon, CO, and NOx emissions within about four minutes from engine start-up. As the components of exhaust system 100 continue to heat-up, catalyst functionality (if present) on particulate matter control device 18 becomes active. For example, in embodiments in which particulate matter control device 18 is provided with a three-way catalyst (TWC) precious metal and wash coat formulation, the particulate matter control device 18 helps to further convert hydrocarbon, CO, and NOx emissions, while simultaneously capturing solid particulate matter in the exhaust gasses. With additional engine operation time, the NOx control system 16 downstream of the particulate filter reaches its minimum operating temperature and begins reducing NOx in the exhaust gasses. At this point, engine 12 can begin operating in lean-burn combustion mode, thus providing improved fuel economy and better performance (e.g. torque and horsepower) that come from lean-burn combustion. Although conventional three-way catalysts (TWC) are relatively ineffective for NOx control under lean combustion conditions (due to excessive amounts of O₂ in the lean-burn emissions), they remain effective for HC and CO oxidation. Thus, in lean-burn conditions, NOx is controlled by the combination of close-coupled catalyst 14 and NOx control system 16, together with any catalyst functionality provided on particulate matter control device 18.

Data in Table 2 show the effectiveness of the uncatalyzed wall flow filters tested in the system configuration of FIG. 2. The measured filtration efficiencies in Table 2 are based on accumulation mode particle numbers (e.g. the number of carbonaceous soot and inorganic ash particles), nucleation mode particle numbers (e.g., the number of aerosolized gasoline and oil particles), and particle mass. Samples A, D and H of Table 2 are of the same configuration as Samples A, D and H described with reference to Table 1. As seen in the data of Table 2, filtration efficiencies in excess of 90% (based on particle number and particle mass, alone and in combination) may be achieved.

It will be apparent to those skilled in the art that various modifications and variations can be made to the described embodiments without departing from the spirit and scope of the invention as claimed. Thus it is intended that modifications and variations of embodiments described herein encompass the invention, provided such modifications and variations come within the scope of the appended claims and their equivalents. 

1. An exhaust gas after-treatment system for a gasoline engine comprising: a three-way catalyst close-coupled to the gasoline engine; a particulate matter control device positioned downstream of the three-way catalyst; and a NOx control system positioned downstream of the particulate matter control device.
 2. The exhaust gas after-treatment system of claim 1, wherein the NOx control system comprises one or more of a lean NOx trap, a lean NOx catalyst, and a selective catalytic reduction catalyst.
 3. The exhaust gas after-treatment system of claim 2, wherein the NOx control system comprises a combination of a lean NOx trap and a selective catalytic reduction catalyst.
 4. The exhaust gas after-treatment system of claim 1, wherein the particulate matter control device comprises a wall-flow filter.
 5. The exhaust gas after-treatment system of claim 4, wherein the wall-flow filter comprises a porous ceramic honeycomb body.
 6. The exhaust gas after-treatment system of claim 1, wherein the particulate matter control device comprises one of cordierite, aluminum titanate, silicon carbide, and mullite.
 7. The exhaust gas after-treatment system of claim 5, wherein the porous ceramic honeycomb body comprises a cell density in the range of about 200 to about 600 cpsi, a wall thickness in the range of about 3 mil to about 20 mil and a total wall porosity in the range of about 30% to about 60%.
 8. The exhaust gas after-treatment system of claim 5, wherein the ceramic honeycomb body is comprised of alternately plugged inlet channels and outlet channels, the inlet channels having a larger hydraulic diameter than the outlet channels.
 9. The method of claim 1, wherein the exhaust gas after-treatment system reduces particles emitted by a gasoline engine to less than about 6×10¹¹ particles/km when measured by the PMP protocol over the NEDC regulatory drive cycle.
 10. A method for cleaning an engine exhaust gas flow, comprising: operating a gasoline engine in a stoichiometric condition upon start-up of the engine; conducting an exhaust gas flow generated by the engine through an exhaust system comprising, successively, a flow-through substrate having a three-way catalytic coating, a wall-flow particulate filter, and a NOx control system; and operating the gasoline engine in a lean-burn condition after the NOx control system attains a minimum operating temperature.
 11. The method of claim 10, wherein the gasoline engine is operated at a compression ratio of less than about
 15. 12. The method of claim 10, wherein the gasoline engine is spark ignited.
 13. The method of claim 10, wherein the engine produces soot at less than about 1×10¹³ particles/km when measured by the PMP protocol over the NEDC regulatory drive cycle.
 14. The method of claim 10, wherein the exhaust system reduces emitted particles to less than about 6×10¹¹ particles/km when measured by the PMP protocol over the NEDC regulatory drive cycle.
 15. The method of claim 10, wherein the wall-flow particulate filter has a catalytically active coating.
 16. The method of claim 10, wherein the NOx control system comprises one or more of a lean NOx trap, a lean NOx catalyst, and a selective catalytic reduction catalyst.
 17. The method of claim 10, wherein the flow-through substrate is close-coupled to the engine.
 18. The method of claim 10, wherein the wall-flow particulate filter has a cell density in the range of about 200 to about 600 cpsi, a wall thickness in the range of about 3 mil to about 20 mil, and a total wall porosity in the range of about 30% to about 60%. 